2.4.2. Cyclic loess normalization

This stabilizes the MVD between slides by applying a pairwise non-linear local regression (LOESS). It utilizes a pseudo Bland-Altman (MA) plot defined as the average [A] versus the difference [M] between the intensities on two independent slides, repeated for N number of slides [29]. It yields an ‘average’ array that is used as a reference to adjust the MVD across all slides. It can be applied to both raw and log-transformed data [30]. Cyclic loess performs a pairwise normalization on all distinct pairs of slides utilising the MA plot and LOESS smoothing. The MA plot in single-colour microarrays for a pair of arrays is the scatter plot of average the intensity values [A] from both arrays vs. difference in expression values [M] of the same arrays The intensity-dependent differences are first estimated and the differences subsequently regulated by centering the LOESS line to zero [26], [29].

Given yijkr⌢ for a given slide i=1,2,3,.....,n,Mr=log2y1jkr⌢/y2jkr⌢ and Ar=12log2y1jkr⌢×y2jkr⌢ where r=1,2,3,...,p are the spot intensities for a specific protein. A LOESS curve is then fitted for the MA differences and Mr′ a normalised value for Mr is generated. The spot for each specific protein intensities is normalized as follows y^1jkr′=2Ar+Mr′2 and y^2jkr′=2Ar-Mr′2 or the logarithm transformed equivalents [29], [31]. Here we use the LOESS method of Ballman et al. [8], [29].

The underlying assumption in cyclic loess is that there is minimal variation between individual arrays under the conditions being studied. Its application for protein microarray experiments designed to detect high levels of variation in different arrays may thus be limited. We recommend the randomization of samples during the design of the study to ensure there is minimal variation between the arrays.